It is recommended that production systems running AR System on Windows be 64-bit. Thus, it would be recommended that you migrate to new HW that is 64-bit rather than upgrading in place on your 32-bit system.

It is not clear from your question whether your "cusotmizations" are to ITSM applications of if you are a custom-only shop. If the former (i.e. you've modified ITSM applications), it would be recommended that you migrate rather than upgrade because the ITSM applications have changed quite a bit between 6.x and 7.x.

Because the Best Practice Customization Utility does not currently support the 6.x versions of products, it would be recommended that you migrate rather than upgrade to take advantage of overlays in 7.6.04. This also gives you a chance to review your customizations and determine if they really need to be carried forward.